Time Series Decompisiotion

1 Introduction

1.1 Data description

This data set shows the bikers on Brooklyn Bridge 7 days of the week compared to the number on all bridges to give us the rate that bikers travel the Brooklyn bridge.

1.2 Define time series object

Since this is monthly data, frequency =7 will be used the define the time series object because there are 7 days of the week.

US bond monthly rates

2 Forecasting with Decomposing

Notice that the classical decomposition method does not work as well as the STL method due to the robustness of the LOESS component. The following visual representations show the different behaviors of the two methods of decomposition.

Classical decomposition of additive time series

STL decomposition of additive time series

Training and Testing Data

We hold up the last 4 periods of data for testing. The rest of the historical data will be used to train the forecast model.

We split the training into 4 different groups and test them.

We next perform error analysis.

Error comparison between forecast results with different sample sizes

	MSE	MAPE
n.11	0.0003780	0.1045434
n.8	0.0003767	0.1040872
n. 8	0.0006108	0.1473792
n. 4	0.0003912	0.1148960

The n=11 and the first n=8 have similar mean squared errors 0.0003780 and 0.0003767. They also have very similar Mean absolute percentage errors with 0.1045434 and 0.1040872 respectively

2.1 Error Curves

Comparing forecast errors

The graph above shows the error curves for the different models. you can see that first two have the lowest error and are roughly the same numbers.